Answer:
The probability is 0.0192 to four decimal places.
Step-by-step explanation:
In this question, we are asked to calculate the probabilities that three events will occur at the same time.
Firstly, we identify the individual probabilities.
The probability of 6 showing In a throw of die is 1/6
The probability of a coin showing head in a flip of coin is 1/2
The probability of a face card being drawn in a deck of cards is 12/52( There are 12 face cards in a deck of cards)
Mathematically to get the probability of all these events happening, we simply multiply all together.
This will be ;
1/6 * 1/2 * 12/52 = 1/52 = 0.0192 ( to 4 decimal place)
Answer:
Step-by-step explanation:
We have the equations
4x + 3y = 18 where x = the side of the square and y = the side of the triangle
For the areas:
A = x^2 + √3y/2* y/2
A = x^2 + √3y^2/4
From the first equation x = (18 - 3y)/4
So substituting in the area equation:
A = [ (18 - 3y)/4]^2 + √3y^2/4
A = (18 - 3y)^2 / 16 + √3y^2/4
Now for maximum / minimum area the derivative = 0 so we have
A' = 1/16 * 2(18 - 3y) * -3 + 1/4 * 2√3 y = 0
-3/8 (18 - 3y) + √3 y /2 = 0
-27/4 + 9y/8 + √3y /2 = 0
-54 + 9y + 4√3y = 0
y = 54 / 15.93
= 3.39 metres
So x = (18-3(3.39) / 4 = 1.96.
This is a minimum value for x.
So the total length of wire the square for minimum total area is 4 * 1.96
= 7.84 m
There is no maximum area as the equation for the total area is a quadratic with a positive leading coefficient.
Answer:
Step-by-step explanation:
The given expression is
The tangent of -1 is defined, it's around -0.02.
The tangent is a trigonometric function with a period of 
, where each period is separated by a vertical asymptote which indicates that the function is not determined through all its domain, that's what the question refers to when it says "if is undefined, enter undefined".
However, at 
, the tangent is determined, that means, there's no asymptote on that coordinate, that's why it has a "determined value", which is -0.02 approximately.
Combine the fractions by finding a common denominator.
10r+9/r(r+3)
2/3 , 3/4 7/12 there you go
